Simplify the following expression: $\dfrac{2k^3}{6k^2}$ You can assume $k \neq 0$.
Answer: $ \dfrac{2k^3}{6k^2} = \dfrac{2}{6} \cdot \dfrac{k^3}{k^2} $ To simplify $\frac{2}{6}$ , find the greatest common factor (GCD) of $2$ and $6$ $2 = 2$ $6 = 2 \cdot 3$ $ \mbox{GCD}(2, 6) = 2 $ $ \dfrac{2}{6} \cdot \dfrac{k^3}{k^2} = \dfrac{2 \cdot 1}{2 \cdot 3} \cdot \dfrac{k^3}{k^2} $ $\phantom{ \dfrac{2}{6} \cdot \dfrac{3}{2}} = \dfrac{1}{3} \cdot \dfrac{k^3}{k^2} $ $ \dfrac{k^3}{k^2} = \dfrac{k \cdot k \cdot k}{k \cdot k} = k $ $ \dfrac{1}{3} \cdot k = \dfrac{k}{3} $